This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Given the position vector: r(t) = (((t)/(2))i + ((t)/(2))j) \, m To differentiate this vector, we differentiate each component with respect to t. This will give us the velocity vector v(t). Step 1: Differentiate the i component. Using the chain rule, (d)/(dt)((kt)) = -k(kt). Here, k = (1)/(2). (d)/(dt)(((t)/(2))) = -(1)/(2)((t)/(2)) Step 2: Differentiate the j component. Using the chain rule, (d)/(dt)((kt)) = k(kt). Here, k = (1)/(2). (d)/(dt)(((t)/(2))) = (1)/(2)((t)/(2)) Step 3: Combine the differentiated components to form the velocity vector. v(t) = drdt = (-(1)/(2)((t)/(2))i + (1)/(2)((t)/(2))j) \, m/s v(t) = (1)/(2)(-((t)/(2))i + ((t)/(2))j) \, m/s Send me the next one 📸